To illustrate the power of partial classes, we comment that the fundamental class of \(d\) -dimensional halfspaces with margin \(\gamma > 0\)  and \(k\)  labels can be cast as a partial class \(\mathcal {H}_\gamma = \lbrace  h_W : W \in \mathbb {R}^{k \times d} \rbrace \) , where \(h_W(x) = i \in [k]\)  if \((W_i - W_j) \cdot x \ge \gamma \)  for all \(j \ne i\)  and \(h_W(x) = \star \)  otherwise [1]}. As another example,
we can express the constraint that the data have to be
in a low-dimensional space by considering the partial concept class \(\mathcal {H}= \left\lbrace h:\mathbb {R}^d \rightarrow \lbrace 0,1,...,k,\star \rbrace :\mathrm {dim}\left(\mathrm {supp}(h) \right) \ll d \right\rbrace \) , where \(\mathrm {dim}(S)\)  captures the dimension of the set of points in \(S\) .
